Polyphase Sequences Research Articles

Bat Chirps With Good Properties: Zak Space Construction of Perfect Polyphase Sequences

Previously, a discretization of the linear FM chirp of length N=KL 2, L and KL isin Z, was given and the conditions for its minimal Zak space support were derived. Chirps satisfying these conditions are known as finite chirps. In this work, subsets of finite chirps of length N=L 2, L a prime, are examined. The investigation leads to a new, Zak space construction of general polyphase sequence sets of size L-1 with optimal auto and cross-correlation properties, known as perfect sequence sets. It is shown that perfect sequence sets are closely related to sets of finite chirps and, in particular, include the sets of Zadoff-Chu sequences (which are identical with subsets of finite chirps) and the sets of generalized Frank sequences (which are identical with sets of modulations of finite chirps), as special cases. The entire collection of perfect sequence sets is then given by a partition of the set of perfect auto correlation sequences, obtained by right coset decomposition of the group of all permutations with respect to a certain cyclic group. The construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group.

New Perfect Polyphase Sequences and Mutually Orthogonal ZCZ Polyphase Sequence Sets

In communication systems, ZCZ sequences and perfect sequences play important roles in removing multiple-access interference (MAI) and synchronization, respectively. Based on an uncorrelated polyphase base sequence set, a novel construction method, which can produce mutually orthogonal (MO) ZCZ polyphase sequence (PS) sets and perfect PSs, is presented. The obtained ZCZ PSs of each set are of ideal periodic cross-correlation functions (PCCFs), in other words, the PCCFs between such two different sequences vanishes, and the sequences between different sets are orthogonal. On the other hand, the proposed perfect PSs include Frank perfect PSs as a special case and the family size of the former is quite larger than that of the latter.

Discrete frequency-coded radar signal design

A modified simulated annealing algorithm (MSAA) is proposed as combinatorial multivariable optimisation technique to design discrete frequency-coding (DFC) sequence sets with good auto- and cross-correlation properties. The proposed algorithm is a combination of simulated annealing and Hamming scan algorithm. MSAA has global minimum estimation capability of simulated annealing and fast convergence rate of Hamming scan algorithm. Some of the synthesised results are presented, the properties of the sequence sets are shown to be better than the other sequence sets known in the literature. Synthesised DFC sequence sets have properties far better than polyphase sequence sets. The synthesised DFC sequence sets are promising for practical application to netted radar/multiple radar systems.

A DSP Approach for Finding the Codon Bias in DNA Sequences

The detection of different forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have primarily focussed on assigning numerical values to the symbolic DNA sequence and then applying spectral analysis tools such as the short-time discrete Fourier transform (ST-DFT) to locate these repeats. A key application of DNA periodicity finding has been in the identification of the protein coding regions in DNA sequences by tracking the so-called period-3 component using the DNA spectrum. The main problem with this gene detection approach is that it is successful for certain genes but does not work for others. An interesting open research problem is to therefore determine the underlying reasons behind this disparity in performance. This requires, in turn, a solid understanding of the working principles of the period-3 component and the DNA spectrum. In this paper, we present a DSP-based approach that provides a complete analysis of this phenomenon. Specifically, we derive a new DSP based model that 1) clearly explains the underlying mechanism of the period-3 component, 2) directly relates the identification of the period-3 component to the detection of nucleotide bias in the codon structure, and 3) completely characterizes the DNA spectrum by a set of numerical sequences termed the filtered polyphase sequences. Furthermore, by adhering to the specific structure of the derived model, we can show that standard signal processing tools such as digital filtering can substantially enhance the detection of the codon bias. Several performance measures of DNA periodicity detection are also proposed and experimental results are provided to illustrate the key findings of our work.

Perfect polyphase sequences with small alphabet

New perfect polyphase sequences with a small phase alphabet and some zero elements are proposed. These sequences are derived from pairs of perfect polyphase sequences with zeroes and odd-perfect ternary sequences of the same length N. They have a length of 4N and possess a peak factor close to 1 as N becomes large. The sequences can be used in digital communication, navigation and radar engineering.

Long polyphase sequences for adaptive MMSE detector in asynchronous CDMA PLC system

An adaptive receiver solution for an asynchronous DS-CDMA system in an indoor powerline network is proposed. A combination of different receiver structures with binary and complex-polyphase sequences is evaluated and compared in terms of bit error rate. The simulation results based on a complete powerline channel model are reported.

MIMO ISI Channel Estimation Using Uncorrelated Golay Complementary Sets of Polyphase Sequences

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, optimal training sequence design for multiple-input multiple-output (MIMO) intersymbol interference channels is addressed, and several novel low-complexity channel estimators are proposed, using uncorrelated Golay complementary sets of polyphase sequences.<footnoteref refid="fnote1"/><footnote id="fnote1"> <footnotepara>A polyphase sequence is a sequence of complex numbers, each of unit magnitude.</footnotepara> </footnote> The theoretical analysis and simulation show that, when the additive noise is Gaussian, the proposed best linear unbiased estimator achieves the minimum possible classical CramÉr–Rao lower bound (CRLB) if the channel coefficients are regarded as unknown deterministics. On the other hand, the proposed linear minimum mean-square error estimator attains the minimum possible Bayesian CRLB when the underlying channel coefficients are Gaussian and independent of the additive Gaussian noise. The proposed channel estimators not only achieve the best estimation performance but can also be implemented with low complexity via DSP or application-specified integrated circuit/field programmable gate array. This has been possible due to the special structures intrinsic to uncorrelated Golay complementary sets of polyphase sequences, which make the proposed channel estimators ready to use in the practical MIMO systems. </para>

New Method of Chaotic Polyphase Sequences Design

A new polyphase sequences synthesis method based on chaotic maps is presented. The correlation properties of sequences designed using this method are analyzed and proved to be almost perfect. The phase alphabet size can be any positive non-zero even, and the alphabet elements can be chosen arbitrarily by users. Simulation results show the effectiveness of this polyphase sequences design method.

Polyphase Radar signal Design Using Modified Simulated Annealing Algorithm

In this paper a Modified Simulated Annealing Algorithm (MSAA) is proposed as a statistical technique for obtaining approximate solutions to combinatorial optimization problems. The proposed algorithm is a combination of Simulated annealing and Hamming scan algorithm. It is used to design polyphase sequence sets which have good autocorrelation and cross correlation properties. Some of the synthesized results are presented, and the properties of the sequence sets are shown to be better than other sequence sets known in the literature. The synthesized polyphase sequence sets are promising for practical application to orthogonal netted radar systems/multiple radar systems. The convergence rate of the algorithm is also shown to be good.

Optimizing Polyphase Sequences for Orthogonal Netted Radar

Orthogonal netted radar transmitter signals require a very low aperiodic autocorrelation peak sidelobe level (PSL), low aperiodic cross-correlation, and a good resilience to small Doppler shifts. A new set of polyphase sequences is presented with good correlation properties as well as resilience to Doppler shifts. These sequences are built using numerical optimization based on correlation properties. A structural constraint is imposed on the optimized polyphase sequences, which maintains Doppler tolerance. Cross entropy (CE) technique is used to optimize the sequences. Correlation and Doppler results are compared with best-known sequences on various merit factors and shown to be superior

A New Class of Polyphase Sequence Sets with Optimal Zero-Correlation Zones

This paper proposes a new class of polyphase ZCZ (zero-correlation zone) sequence sets which satisfy a mathematical upper bound. The proposed ZCZ sequence sets are obtained from DFT matrices and unitary matrices. In addition, this paper discusses the cross-correlation property between different ZCZ sequence sets which belong to the proposed class.

Polyphase Sequences With Low Autocorrelation

Low autocorrelation for sequences is usually described in terms of low base energy, i.e., the sum of the sidelobe energies, or the maximum modulus of its autocorrelations, a Barker sequence occurring when this value is /spl les/ 1. We describe first an algorithm applying stochastic methods and calculus to the problem of finding polyphase sequences that are good local minima for the base energy. Starting from these, a second algorithm uses calculus to locate sequences that are local minima for the maximum modulus on autocorrelations. In our tabulation of smallest base energies found at various lengths, statistical evidence suggests we have good candidates for global minima or ground states up to length 45. We extend the list of known polyphase Barker sequences to length 63.

A generation method of orthogonal periodic complex number sequence sets with lowest peak of cross‐correlation for any period based on chirp sequences

AbstractIn this paper, we propose a new generation method of orthogonal periodic complex number sequence sets based on chirp sequences that can derive the orthogonal periodic complex number sequence set having the minimum cross‐correlation peak for any period. First, we use the Ohue–Okahisa Conjecture that is proven in a practical range related to the orthogonal periodic polyphase sequence obtained by taking the inverse discrete Fourier transform of a chirp sequence to derive the relationship between the period N having the minimum peak of the cross‐correlation and the chirp sequence parameter R, and clearly explain a generation method of an orthogonal periodic complex number sequence pair having the minimum cross‐correlation peak for any period. Next, we present a generation method of the orthogonal periodic complex number sequence set having the minimum cross‐correlation peak for any two sequences in the set. The dimension of this set is clearly equal to the minimum prime factor of the period N. Furthermore, we present a generation method of the orthogonal periodic polyphase sequence set having the minimum cross‐correlation peak for any period and show that the dimension of this set becomes a value 1 less than the minimum prime factor of period N. We show that this generation method can derive the orthogonal periodic complex number sequence set having the minimum cross‐correlation peak for periods that could not be generated by conventional techniques and can derive the orthogonal periodic polyphase sequence set demonstrated previously. Finally, we present a generation example of the orthogonal periodic sequence set having the minimum cross‐correlation peak and clearly show that the orthogonal periodic complex number sequence set and orthogonal periodic polyphase sequence set having the minimum cross‐correlation peak can be generated. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(5): 1–11, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10129

Modified Walsh‐Hadamard sequences for DS CDMA wireless systems

AbstractWe propose a simple but efficient method for modifying Walsh–Hadamard sequences to achieve correlation properties suited for asynchronous DS CDMA applications. The proposed method can be used to minimize the mean square value of aperiodic cross‐correlation or the mean square value of aperiodic autocorrelation, the maximum value of aperiodic cross‐correlation functions, merit factor or other properties of the sequence set. The important feature of the method is that it modifies correlation properties of the sequence set, while preserving their orthogonality for the perfect synchronization. The proposed method can be applied to obtain bipolar, quadri‐phase, or general polyphase sequences. Copyright © 2002 John Wiley &amp; Sons, Ltd.

A new polyphase sequence with perfect even and good odd cross-correlation functions for DS/CDMA systems

A class of polyphase signature sequences for direct-sequence code-division multiple-access (DS/CDMA) systems is proposed. The proposed class has zero periodic (=even) cross-correlation (CC) function and approximate maximum magnitude N//spl pi/ of odd cross-correlation (OCC), where N is the length of sequences. Although the maximum magnitude is relatively large, it is observed that the maximum magnitude has little effect on the performance of the DS/CDMA system, since its frequency is very low. The performance of the proposed sequence in DS/CDMA systems is investigated and shown to be better than that of other sequences for an asynchronous additive white Gaussian noise channel environment with and without Rayleigh multipath fading.

Linear complexity of polyphase power residue sequences

The well known family of binary Legendre or quadratic residue sequences can be generalised to the multiple-valued case by employing a polyphase representation. These p-phase sequences, with p prime, also have prime length L, and can be constructed from the index sequence of length L or, equivalently, from the cosets of pth power residues and non-residues modulo-L. The linear complexity of these polyphase sequences is derived and shown to fall into four classes depending on the value assigned to b0, the initial digit of the sequence, and on whether p belongs to the set of pth power residues or not. The characteristic polynomials of the linear feedback shift registers that generate these sequences are also derived.

A statistical analysis of random polyphase signature sequences in multipath fading DS-CDMA channels

Direct sequence code division multiple access (DS-CDMA) communication systems using random polyphase sequences with coherent reception in multipath fading channels are considered. By examining the asymptotic characteristics of the multiple access interference and multipath interference, we show that the DS-CDMA system performance with random m p -phase sequences of m p ⩾3 is better than that with random binary sequences in multipath fading environment.

Transmitter adaptation in multicode DS-CDMA systems

The problem of transmitter adaptation in the form of adapting the spreading sequences and the transmission powers of different users for a multicode direct-sequence code division multiple access (DS-CDMA) system is considered. Particular attention is given to a distributed algorithm, which updates each pair of transmitter and receiver without information from other users. The transmitter adaptation problem and the algorithm are studied from the viewpoint of a single user, as well as the viewpoint of the whole system. The algorithm is shown to give either the optimal sequences or a choice of sequences that is close to the optimal one. Simulation results show that major improvement in performance can be obtained with the proposed transmission adaptation scheme. The effect of restricting the choice of sequences to polyphase sequences is also considered.

Multiple-access interference reduction for QS-CDMA systems with a novel class of polyphase sequences

In this paper, a new class of polyphase sequences for CDMA systems and its generation method are suggested, and the correlation properties of the sequence are investigated. The performance of the sequence in quasi-synchronous CDMA (QS-CDMA) systems is investigated under a frequency-selective, time-nonselective, slow Nakagami fading channel with additive white Gaussian noise (AWGN). It is shown that the performance of the QS-CDMA systems using the suggested sequence is independent of the number of users and is much better than that using the PN sequence.

Generalised Sidelnikov sequences with optimal autocorrelationproperties

A new class of almost binary and polyphase sequences with optimum periodic correlation properties is introduced. This class forms a generalisation of sequences already described by Sidelnikov (1969) and Lempel et al. (1997).